Question: Simplify the following expression: $ t = \dfrac{10}{7} - \dfrac{4y + 6}{y + 9} $
Solution: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{y + 9}{y + 9}$ $ \dfrac{10}{7} \times \dfrac{y + 9}{y + 9} = \dfrac{10y + 90}{7y + 63} $ Multiply the second expression by $\dfrac{7}{7}$ $ \dfrac{4y + 6}{y + 9} \times \dfrac{7}{7} = \dfrac{28y + 42}{7y + 63} $ Therefore $ t = \dfrac{10y + 90}{7y + 63} - \dfrac{28y + 42}{7y + 63} $ Now the expressions have the same denominator we can simply subtract the numerators: $t = \dfrac{10y + 90 - (28y + 42) }{7y + 63} $ Distribute the negative sign: $t = \dfrac{10y + 90 - 28y - 42}{7y + 63}$ $t = \dfrac{-18y + 48}{7y + 63}$